Ms Boyack, who is currently finalising Labour’s devolution proposals, hinted that city deals and further devolution to the islands would feature in Labour’s offering when it is unveiled at the party’s conference next week.

Ms Sturgeon said her officials are already in discussions for a city deal for Glasgow but said there is a danger that it could hit the overall Scottish Budget.

She was jeered when she suggested the SNP’s council-tax freeze had not removed power from local government, insisting they still have a choice if they are willing to accept a cut in funding from central government.

Liberal Democrat leader Willie Rennie said the SNP’s mantra that the best people to make decisions about Scotland’s future are the people who live there “is a compelling argument”, but that it must extend to local communities.

Ms Boyack said: “You can absolutely look forward to more devolution if we are all part of the UK on September 19 to the Scottish Parliament and local government.

“Our committee will be reporting next week, so I cannot reveal to you the radical nature of our recommendations. I’d have to shoot you all if I told you anything!

“But I hope I can give you a sense of direction. I’m very grateful to those of you who have sent in submissions on city deals and ‘our islands, our future’ discussions.

“It’s not just about giving local government responsibility or power, but also giving local government income stream to go with them.

“I think some of the really exciting discussions have been about city deals, looking at how you empower local government to build up a series of services, for example looking at getting people out of long-term unemployment.”

Ms Sturgeon said: “I don’t believe in independence just to transfer powers from Westminster to Holyrood.

“I believe those powers should be transferred further down to local level and I think one of the opportunities for you in this debate is to challenge us.

“If we get more powers in Holyrood, which of these powers would it be right to devolve down to your hands?

“Scottish Government officials have been talking to officials in Glasgow, and indeed the UK Government, about the developing thinking around a possible city deal for Glasgow, and we are supportive of that as long as it’s developed in such a way that doesn’t lead to a situation where this is a hit on Scotland’s Budget, which is one of the dangers.”

She added: “There has been no legislative removal of power from local government.

“The deal is if you freeze council tax you get a share of £70 million to compensate for the money you won’t raise from council tax, but you can choose to put council tax up instead of getting the share of the £70 million.”

Mr Rennie said: “If any UK minister was to tell Nicola how to set her £30 billion budget you may hear about it, but local government often is quite tolerant and understanding when Scottish ministers interfere in how you spend your money.

“Nicola says the best people to make decisions about the future of our country are the people who live here.

“It’s quite a compelling argument. I think it’s an argument that in partnership should be made at a local level, just like in partnership it should be made in the Scottish Parliament.”

Conference also heard from statistician John Curtice on the direction of the polls in the independence referendum.

Recent polls have shown a modest swing towards independence since the publication of the White Paper, which appears to have convinced more people to move from undecided to Yes, he said.

But the numbers would not be enough to attain an overall Yes vote without a swing from No, and the polls also indicate more people may be inclined to swing away from Yes to No than the other way round, he added.